Common Functional Implied Volatility Analysis

Functional Principal Component Analysis (FPCA) has become a widely-used dimension reduction tool for functional data analysis. When additional covariates are available, existing FPCA models integrate them either in the mean function or in both the mean function and the covariance function. However, methods of the first kind are not suitable for data that display second-order variation, while those of the second kind are time-consuming and make it difficult to perform subsequent statistical analyses on the dimension-reduced representations. To tackle these issues, we introduce an eigen-adjusted FPCA model that integrates covariates in the covariance function only through its eigenvalues. In particular, different structures on the covariatespecific eigenvalues -corresponding to different practical problems -are discussed to illustrate the model's flexibility as well as utility. To handle functional observations under different sampling schemes, we employ local linear smoothers to estimate the mean function and the pooled covariance function, and a weighted least square approach to estimate the covariate-specific eigenvalues. The convergence rates of the proposed estimators are further investigated under the different sampling schemes.

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Common Functional Implied Volatility Analysis

Cited by 7 publications

References 10 publications

DSFM fitting of implied volatility surfaces

DSFM fitting of implied volatility surfaces

A survey of functional principal component analysis

Eigen-Adjusted Functional Principal Component Analysis

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